Extension of the generalized linear model where a continuous variable's effect is an estimated smooth function rather than a single coefficient, revealing U-shaped effects that banding hides.
A generalized linear model forces driver age into a linear effect, which is false, or into bands, which is arbitrary and produces unjustifiable premium jumps between two birthdays. The generalized additive model replaces the coefficient with an estimated smooth function, typically a penalized spline basis whose roughness is controlled by a smoothing parameter chosen by validation. The result is a continuous curve that lets the data speak: motor claims experience against age traces a sharp U, high for young drivers, low between thirty-five and sixty, then rising again. Three advantages follow: a premium continuous in age hence free of threshold effects, less need for bands decided in advance, and a visual diagnosis that can then inform banding if production constraints require it. The cost is regulatory and commercial legibility: a rating table can be communicated, a spline has to be plotted, and monotonicity constraints often have to be imposed by hand for the rate to stay defensible.
Motor frequency model, 2026 year. The generalized additive model on age returns a relative frequency of 2.1 at nineteen, 1.0 at forty-five, and 1.24 at seventy-eight, with the upturn starting near seventy-two. The five-band split used until then placed the top boundary at sixty-five and therefore missed the upturn entirely, diluting it into a single band of sixty-five and over.
GAM, generalized additive model, splines de régression, effet non linéaire lissé